PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
8001Phi(64736,139)55959Enzo Doria07/2012
800215215^4762+4762^1521555958Hans Havermann03/2016
800319317^788+788^1931755953Anatoly F. Selevich12/2006
800413582^13165+13165^1358255950Hans Havermann08/2016
8005(78557*2^185842+1)/18955947Lelio R Paula06/2014
800615^47562-8655938Lelio R Paula02/2013
80073^117222+455930Lelio R Paula03/2012
800824^40519-23^4051955925Robert Price07/2012
800913636^12623+12623^1363655924Hans Havermann07/2016
80102^185767-9955922Lelio R Paula03/2011
8011(19*2^185750-1)/1555917Lelio R Paula01/2014
801215^47542-5855914Lelio R Paula02/2013
801320^42973-558355910Enzo Doria03/2013
80144*10^55906+2155907Robert Price08/2016
80152^185713-11155906Lelio R Paula03/2011
801613^50174+8855891Lelio R Paula01/2013
801714569^6846+6846^1456955879Hans Havermann08/2016
8018Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
80193^117087-8055865Lelio R Paula10/2012
8020(7*10^55851-43)/955851Robert Price10/2014
80212^185519-16955847Lelio R Paula03/2011
80227^66074+1055840Lelio R Paula10/2012
8023(19*10^55833-49)/355834Robert Price02/2017
8024(2*10^55834-59)/355834Robert Price05/2017
802512^51732+555829Lelio R Paula01/2013
80263*2^185429+755821Lelio R Paula03/2014
8027(9787*2^185420-1)/38155819Lelio R Paula04/2015
802814427^7396+7396^1442755819Hans Havermann08/2016
802910^55811+2155812Robert Price01/2011
803010^55811-7410355811Patrick De Geest12/2012
803111^53591-153055810Enzo Doria11/2012
80322^185355-214555798Lelio R Paula03/2011
803314531^6912+6912^1453155794Hans Havermann07/2016
80342^185327-161555789Lelio R Paula03/2011
80352^185280-1277955775Enzo Doria10/2012
803615504^3955+3955^1550455771Hans Havermann07/2016
8037(2*10^55762-59)/355762Robert Price05/2017
80385^79770-4455757Lelio R Paula10/2012
803918^44416-8555755Lelio R Paula02/2013
80402^185208-45999555754Enzo Doria06/2015
80412^185200+118555751Lelio R Paula03/2011
80427^65964+6^(65964-1)55747Robert Price03/2016
80432^185151-23715755737Gary Barnes09/2009
8044110017^11055-10255734Enzo Doria07/2012
804514754^5987+5987^1475455729Hans Havermann07/2016
804640090!3-955711Robert Price09/2014
80479*10^55707+8955708Robert Price11/2016
80482^185023-225755698Yves Minet06/2009
804918628^977+977^1862855696Anatoly F. Selevich01/2007
80502^185006-9355693Lelio R Paula03/2011
80512^185003-251555692Yves Minet07/2014
80526^71524-1955657Lelio R Paula10/2012
80532^184872-219555653Yves Minet08/2013
8054507^20572+20572^50755648Norbert Schneider06/2016
8055134^26151-13355626Norbert Schneider03/2015
805615340^4221+4221^1534055614Hans Havermann07/2016
805727743!2+255612Robert Price01/2013
805820^42744+8155612Lelio R Paula02/2013
805914609^6406+6406^1460955611Hans Havermann07/2016
80602^184724-11288355608Enzo Doria06/2014
806113507^13074+13074^1350755601Hans Havermann07/2016
80622^184689+12955597Lelio R Paula03/2011
8063(9179*2^184672-1)/19355594Lelio R Paula03/2015
8064(22*10^55592-19)/355593Robert Price02/2017
8065Phi(59984,89)55582Enzo Doria05/2012
806611^53368+1655578Lelio R Paula01/2013
806720^42717-192355577Enzo Doria03/2013
8068117^26870+26870^11755573Serge Batalov05/2014
806912^51488+5555565Lelio R Paula01/2013
8070(44*10^55558-17)/955559Robert Price06/2015
807110^55555+3285755556Patrick De Geest06/2010
807210^55555-13672155555Patrick De Geest06/2010
8073(11*2^184541-1)/35155551Lelio R Paula01/2014
807420^42696-204355549Enzo Doria03/2013
8075(2*10^55544+1)/355544Serge Batalov06/2009
8076(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
80775003^15013-16055537Enzo Doria07/2012
807839^34896-255522Lelio R Paula08/2013
8079(6^71345-61)/555517Lelio R Paula05/2014
80802^184407-301955513Yves Minet10/2014
8081(43*10^55512-61)/955513Robert Price06/2015
808220^42667-84355512Enzo Doria03/2013
8083133^26134-13255505Norbert Schneider03/2015
8084(31*2^184378-1)/71155502Lelio R Paula01/2014
80859*7^65667-455497Lelio R Paula09/2014
80862^184342-17355493Lelio R Paula03/2011
808715^47182+9255491Lelio R Paula02/2013
80885^79378+655483Lelio R Paula10/2012
8089581^20068+20068^58155472Norbert Schneider06/2016
8090(2^184232+1)/25755457Donovan Johnson03/2005
809118^44177-141555455Enzo Doria03/2013
80922^184203-279786755451Enzo Doria04/2016
80932^184189+1755447Lelio R Paula03/2011
80942^184183+2612355445Yves Minet01/2010
8095Phi(77077,10)55441Ray Chandler05/2009
80962^184141-11325155432Enzo Doria07/2014
80972^184093-50461355418Gary Barnes09/2009
8098(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
80992^184044-11126955403Enzo Doria05/2014
810014051^8766+8766^1405155401Hans Havermann07/2016
810198^27819+27819^9855394Serge Batalov05/2014
810258046^9+9^5804655390Andrey Kulsha02/2004
81032^183980+7524155384Enzo Doria04/2016
810410^55372+3755373Robert Price01/2011
810510^55372-4996755372Patrick De Geest12/2012
8106(13*10^55367+17)/355368Robert Price06/2015
81072*6^71150+755366Lelio R Paula09/2014
810819^43296-6255365Lelio R Paula02/2013
810919^43295+1055364Lelio R Paula02/2013
8110(29*10^55362-11)/955363Robert Price04/2015
8111(37*10^55359+53)/955360Robert Price05/2015
811219^43283+7255349Lelio R Paula02/2013
81132^183800-6555330Lelio R Paula03/2011
811421001^12801-11055329Enzo Doria07/2012
811533^36433-32^3643355325Robert Price04/2012
8116(17*2^183729+1)/14555308Lelio R Paula07/2012
81189^57952+8^(57952-1)55301Robert Price03/2016
811714872^5229+5229^1487255301Hans Havermann08/2016
811961^30972-255296Lelio R Paula08/2013
81202^183671-11253755291Enzo Doria06/2014
8121(2^183687+7)/49793974555287Lelio R Paula02/2012
81223^115873+5655286Lelio R Paula10/2012
812313^49629-8455284Lelio R Paula01/2013
81242^183632-555279Henri Lifchitz08/2005
812513981^8988+8988^1398155277Hans Havermann07/2016
8126(5*2^183585+1)/1355265Lelio R Paula07/2012
81272^183576+17155262Lelio R Paula03/2011
812813^49604+8255257Lelio R Paula01/2013
8129(11*10^55254+1)/355255Erik Branger03/2014
81303^115802-2655252Lelio R Paula10/2012
81312^183534-364555250Lelio R Paula01/2011
8132(15*2^183533-1)/11355249Lelio R Paula01/2014
81335^79032-1376655241Enzo Doria02/2013
81348*3^115759-755232Lelio R Paula03/2014
81356^70974-13755229Lelio R Paula10/2012
81362^183446-11307355223Enzo Doria07/2014
81372^183441+57729457555222Lelio R Paula03/2013
81385^79000-655219Lelio R Paula10/2012
81392^183413-90155213Yves Minet01/2012
814019^43168-5055202Lelio R Paula02/2013
81412^183340+1968355191Lelio R Paula02/2012
81426^70923+3555189Lelio R Paula10/2012
81432^183317-403555184Lelio R Paula01/2011
81442^183284-1555174Lelio R Paula03/2011
81452^183255+14955166Lelio R Paula02/2011
81464*10^55165+8755166Robert Price05/2016
8147(3^115574+4)/6303755139Lelio R Paula03/2012
81482^183165-11233355139Enzo Doria06/2014
81492^183142+85555132Lelio R Paula01/2011
8150(49*10^55129+383)/955130Robert Price04/2017
81512^183019+25525555095Lelio R Paula01/2011
81523*10^55077+755078Erik Branger11/2013
8153(62*10^55075-71)/955076Robert Price09/2015
815427499!2-3255070Robert Price10/2015
815515307^3958+3958^1530755067Hans Havermann08/2016
815670^29836-6955051Norbert Schneider10/2012
815718^43854-8355049Lelio R Paula02/2013
81587^65126+5855038Lelio R Paula10/2012
81592^182827-161555037Lelio R Paula11/2009
81607*10^55030-955031Dmitry Domanov11/2010
81616^70702+2355017Lelio R Paula10/2012
8162(23*2^182753+1)/15155014Lelio R Paula07/2012
81632^182743-161555012Lelio R Paula11/2009
8164(24737*2^182736+1)/39955011Lelio R Paula05/2014
81653^115280-956855003Enzo Doria02/2013
81662^182656-1284954985Enzo Doria10/2012
81679*19^42995+1654981Curtis Bright05/2015
81682^182627+2842554977Lelio R Paula11/2009
81692^182597-11305354968Enzo Doria07/2014
8170(3^115213+2)/3090672554964Lelio R Paula03/2012
81712^182581-197554963Yves Minet09/2012
817227449!!-1654959Robert Price06/2015
81744^91283-3^9128354958Jean-Louis Charton01/2004
81732^182565+10754958Lelio R Paula11/2009
81752^182560+205354957Lelio R Paula12/2010
81762^182451-18245154924Henri Lifchitz10/2004
81772^182444+8154922Henri Lifchitz10/2005
81782^182433+7410554918Enzo Doria04/2016
817920^42206-524354912Enzo Doria03/2013
81802^182394+8554907Lelio R Paula02/2011
81812^182374-11228754901Enzo Doria06/2014
8182(47^32833-33^32833)/1454899Serge Batalov12/2016
81832^182363-11316754897Enzo Doria07/2014
81842^182359-11222154896Enzo Doria06/2014
8185(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8186(17*2^182274+1)/146754869Lelio R Paula01/2012
818718^43698-554853Lelio R Paula02/2013
81882^182209-189354851Yves Minet09/2012
81892^182194-344354846Yves Minet12/2016
819015023^4468+4468^1502354836Hans Havermann08/2016
81912^182135+9014354829Yves Minet10/2010
81922^182119+7433354824Enzo Doria04/2016
819314289^6860+6860^1428954818Hans Havermann08/2016
81943^114892-114892^354818Norbert Schneider03/2017
81952^182070-4735554809Lelio R Paula01/2011
81963^114869+7654807Lelio R Paula10/2012
81978^60681-60681^854801Norbert Schneider12/2016
81981897^16710+16710^189754777Serge Batalov05/2014
8199Phi(61868,59)54776Enzo Doria04/2012
8200113^26679+254775Lelio R Paula05/2013
82013^114789-7454769Lelio R Paula10/2012
820215^46567+9854768Lelio R Paula02/2013
8203(2*10^54767-71)/354767Robert Price01/2017
8204(21*2^181931-1)/16999754763Lelio R Paula01/2014
82062^181913+2954762Henri Lifchitz06/2005
8205(31*10^54761-121)/954762Robert Price06/2016
82072^181887+18954754Lelio R Paula02/2011
82082^181874+181874^2-154750Robert Price04/2014
8209(2^181865+9)/733954743Lelio R Paula02/2012
82105^78314-9254740Lelio R Paula10/2012
8211(163*10^54727-1)/954729Serge Batalov12/2014
821215^46531+7454725Lelio R Paula02/2013
8213277^22400-34854712Enzo Doria07/2012
82146^70302+10154706Lelio R Paula10/2012
82153^114622-1040854689Enzo Doria02/2013
8217(23*2^181674+1)/48954688Lelio R Paula01/2012
82162^181669-155154688Yves Minet08/2012
8218(57352^11491-1)/5735154676Serge Batalov04/2015
8219(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8220(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
822113^49073+4654665Lelio R Paula01/2013
8222(57042^11491-1)/5704154649Serge Batalov04/2015
822420^42000+7354644Lelio R Paula02/2013
8223(67607*2^181517+1)/165554644Lelio R Paula05/2014
822533*10^54634+754636Robert Price07/2016
822620^41988+6154628Lelio R Paula01/2013
822720^41988-812354628Enzo Doria03/2013
82282^181420+2118154613Yves Minet03/2011
8229(19*10^54608+161)/954609Robert Price07/2016
823019^42696-2454598Lelio R Paula02/2013
8231(74*10^54583+61)/954584Robert Price10/2015
82322^181316-9439554582Lelio R Paula09/2011
823314751^5006+5006^1475154572Hans Havermann08/2016
823414^47609+3954567Lelio R Paula02/2013
82353^114327-7454548Lelio R Paula10/2012
8236gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8237(17*10^54537-47)/354538Robert Price05/2017
82382^181155-1155*18115554534Henri Lifchitz02/2005
8239Phi(61672,83)54533Enzo Doria05/2012
82409*2^181128+754526Lelio R Paula03/2014
824189*10^54518-754520Robert Price03/2017
82422^181090-11324754514Enzo Doria07/2014
824314031^7670+7670^1403154508Hans Havermann08/2016
824414210^6849+6849^1421054505Hans Havermann08/2016
82452^181043-19954500Lelio R Paula02/2011
824612^50499+554498Lelio R Paula01/2013
824712^50491+554489Lelio R Paula01/2013
82486^70016-14554484Lelio R Paula10/2012
824911^52313-960054479Enzo Doria02/2013
82502^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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